Information on Result #732498
Linear OA(25108, 15708, F25, 30) (dual of [15708, 15600, 31]-code), using (u, u+v)-construction based on
- linear OA(2520, 68, F25, 15) (dual of [68, 48, 16]-code), using
- construction X applied to AG(F,49P) ⊂ AG(F,51P) [i] based on
- linear OA(2519, 65, F25, 15) (dual of [65, 46, 16]-code), using algebraic-geometric code AG(F,49P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2517, 65, F25, 13) (dual of [65, 48, 14]-code), using algebraic-geometric code AG(F,51P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,49P) ⊂ AG(F,51P) [i] based on
- linear OA(2588, 15640, F25, 30) (dual of [15640, 15552, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- linear OA(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(25108, 7854, F25, 2, 30) (dual of [(7854, 2), 15600, 31]-NRT-code) | [i] | OOA Folding | |